Effect of loading on the rotational restraint of cold-formed purlins

Cold-formed purlins are restrained in plane of the top flange by connected sheeting both laterally and rotationally. The stiffness of the rotational restraint CD is influenced by external loading of the purlin. Though, simple tests (recommended, i.e. by valid standards) do not cover the influence of loading. It is shown in this paper that the effect of loading on the rotational restraint is different for cold-formed and for hot-rolled purlins. An analytical model was proposed and solved for Z-shaped and C-shaped purlins and for both gravity and uplift loading, and appropriate formulas were derived. The model was based on study of redistribution of contact forces as function of loading q. It is demonstrated that the effect of loading on the stiffness CD is different for the listed cases. Model results are verified with results of numerical simulation.